By Clark M. Thomas
Back in classical Greece – where the best philosophers figured out that the world is round, that atoms exist, and we can never prove what we know – another thinker took up the “paradox of the arrow.” His name was Zeno of Elea, and what he set forth helps us understand how relativity and quantum motions are related.
Zeno asked us to consider an arrow in flight, which he said cannot fly, because at any one time it is at rest. However, it also flies within distance and time to its destination, which means it is also at any one time not at rest, or so it would seem. Is time therefore a unit, or a continuum? Does it proceed in a granular (or quantum) way, or as a stream? If granular, how are the points linked? If as a stream, how do we stop the stream at any point?
Centuries later the Sufis, a mystical offshoot of Islam, presented us with the parable of several blind Sufis who together met an elephant for the first time. Each one was given the opportunity to touch the elephant, and thereby understand what he was touching. One touched the tail, and said an elephant is like a rope. Another touched a leg, and concluded elephants are like trees. Another touched its side, concluding elephants are like walls. One touched his ear, and guessed an elephant is like a large leaf. And so forth. All were right; and all were wrong.
What do Zeno of Elea and the mythical blind Sufis have in common with each other, and with astronomy?
We all are like Zeno and the Sufis. We imagine what we see of the cosmos is a still photo, when in fact it is a moving picture. Our personal vision is a perspective and a time point in the cosmic flow. Fortunately, mathematics and instruments allow us to compare different aspects of the visible universe, improving our guesses about it all. If all the blind Sufis had been allowed to compare their observations they might have gotten much of the essence of an elephant.
Zeno remains more elusive. We struggle, as did Einstein, with the dual concepts of classical and quantum mechanics. How can one reality be dual? We need a bridge. That bridge is “elasticity.” I have earlier explained how the accelerating electron stretches, then pops, as it begins its journey. Lately, electrons have been measured to have a football shape, implying they are stretchable. Even neutrons have been deduced to have a rounded cube shape when compressed in neutron stars.
The world around and above us is also the world inside us. To better understand the universe is to increasingly understand ourselves. But we must always remember what Socrates said (loosely quoted): The more I know, the less I know.